Generally, yes. However, there are a host of issues that should be considered in the development of policy in the area of male versus female competition. You may be surprised to discover that the U.S. Constitution "trumps" Title IX's position on contact sports.
The best policy and position paper on this issue has been developed by the Women's Sports Foundation: "Issues Related to Girls and Boys Competing With and Against Each Other in Sports and Physical Activity Settings".
Prepared by: Donna A. Lopiano, Ph.D., President, Sports Management Resources